If sin x + sin2 x = 1, then write the value of cos8 x + 2 cos6 x + cos4 x.


Given: sin x + sin2x = 1


To find the value of cos8 x + 2 cos6 x + cos4 x.


⇒ sin x = 1 – sin2x


⇒ sin x = cos2x


⇒ cos8x = sin4x, cos6x = sin3x, cos4x = sin2x .


Substituting above values in given equation we get


⇒ sin4x+2 sin3x+ sin2x [(a+b)2 = a2+2ab+b2]


⇒ (sin x + sin2 x)2 = (1)2


⇒ 1


1